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The clarification of the motion alignment mechanism in collective cell migration is an important issue commonly in physics and biology. In analogy with the self-propelled disk, the polarity memory effect of eukaryotic cell is a fundamental candidate for this alignment mechanism. In the present paper, we theoretically examine the polarity memory effect for the motion alignment of cells on the basis of the cellular Potts model. We show that the polarity memory effect can align motion of cells. We also find that the polarity memory effect emerges for the persistent length of cell trajectories longer than average cell-cell distance.Motion alignment plays various roles widely in selfpropelled systems including migrating cells[1], moving organisms [2], molecular motors[3], self-propelled droplets [4] and swarming robots [5]. In particular, the alignment of migrating cells is indispensable for cell organizing in organogenesis, wound healing and immune response [6,7,8]. In these processes, migrating cells exhibit collective behavior commonly observed in self-propelled systems [9,10,11], including various patterns [12,13], active turbulence [14], traveling wave excitation [15]. For the understanding of these behavior, an important issue is to clarify the alignment mechanism as their underlying basis.The alignment mechanisms of other self-propelled systems may give hints for this clarification. In many selfpropelled systems including bird flocking [16,17], the direct aligning-interaction through visual contact is sup-

Morphological regeneration is an important feature that highlights the environmental adaptive capacity of biological systems. Lack of this regenerative capacity significantly limits the resilience of machines and the environments they can operate in. To aid in addressing this gap, we develop an approach for simulated soft robots to regrow parts of their morphology when being damaged. Although numerical simulations using soft robots have played an important role in their design, evolving soft robots with regenerative capabilities have so far received comparable little attention. Here we propose a model for soft robots that regenerate through a neural cellular automata. Importantly, this approach only relies on local cell information to regrow damaged components, opening interesting possibilities for physical regenerable soft robots in the future. Our approach allows simulated soft robots that are damaged to partially regenerate their original morphology through local cell interactions alone and regain some of their ability to locomote. These results take a step towards equipping artificial systems with regenerative capacities and could potentially allow for more robust operations in a variety of situations and environments. The code for the experiments in this paper is available at: github.com/KazuyaHoribe/RegeneratingSoftRobots.